The elliptic mild slope equation is used to simulate linear wave propagation over variable sea bed topography with mild slopes. The governing equation is discretized by the finite difference method. Based on the BI-CG...The elliptic mild slope equation is used to simulate linear wave propagation over variable sea bed topography with mild slopes. The governing equation is discretized by the finite difference method. Based on the BI-CGSTAB technique, an attractive variant bf BI-Conjugate Gradients (BI-CG) method, the obtained linear algebraic system of equations is solved. Numerical experiments show that the BI-CGSTAB method is efficient for solving the elliptic mild slope equation. The results obtained by the BI-CGSTAB-Based method are much the same as those obtained by other authors with different solution methods, but the convergence rate is much faster than that of other methods.展开更多
Numerical treatment of engineering application problems often eventually results in a solution of systems of linear or nonlinear equations.The solution process using digital computational devices usually takes tremend...Numerical treatment of engineering application problems often eventually results in a solution of systems of linear or nonlinear equations.The solution process using digital computational devices usually takes tremendous time due to the extremely large size encountered in most real-world engineering applications.So,practical solvers for systems of linear and nonlinear equations based on multi graphic process units（GPUs）are proposed in order to accelerate the solving process.In the linear and nonlinear solvers,the preconditioned bi-conjugate gradient stable（PBi-CGstab）method and the Inexact Newton method are used to achieve the fast and stable convergence behavior.Multi-GPUs are utilized to obtain more data storage that large size problems need.展开更多
The concept of candidate particle set is introduced in the MPS gridless numerical method to generate neighboring particle set ma- trix, which can reduce the CPU time to 1/11 of that before introduction. The Bi-CGSTAB ...The concept of candidate particle set is introduced in the MPS gridless numerical method to generate neighboring particle set ma- trix, which can reduce the CPU time to 1/11 of that before introduction. The Bi-CGSTAB （bi-conjugate gradient stabilized） algorithm is applied to solving the Poisson pressure equation, by which the solving speed is significantly accelerated. The process of solitary waves propagating over a numerical flume and interacting with a vertical wall is simulated. The simulated results of water surface elevation are in good agreement with the analytical solution as well as the measured data. The predicted maximum values of the run-up of solitary waves with various relative incident wave heights agree well with the measured results.展开更多
基金National Natural Science Foundation of China under grant No.59839330China Postdoctoral Science Foundation
文摘The elliptic mild slope equation is used to simulate linear wave propagation over variable sea bed topography with mild slopes. The governing equation is discretized by the finite difference method. Based on the BI-CGSTAB technique, an attractive variant bf BI-Conjugate Gradients (BI-CG) method, the obtained linear algebraic system of equations is solved. Numerical experiments show that the BI-CGSTAB method is efficient for solving the elliptic mild slope equation. The results obtained by the BI-CGSTAB-Based method are much the same as those obtained by other authors with different solution methods, but the convergence rate is much faster than that of other methods.
文摘Numerical treatment of engineering application problems often eventually results in a solution of systems of linear or nonlinear equations.The solution process using digital computational devices usually takes tremendous time due to the extremely large size encountered in most real-world engineering applications.So,practical solvers for systems of linear and nonlinear equations based on multi graphic process units（GPUs）are proposed in order to accelerate the solving process.In the linear and nonlinear solvers,the preconditioned bi-conjugate gradient stable（PBi-CGstab）method and the Inexact Newton method are used to achieve the fast and stable convergence behavior.Multi-GPUs are utilized to obtain more data storage that large size problems need.
基金This work was supported by the Natural Science Foundation of China under No.50479047.
文摘The concept of candidate particle set is introduced in the MPS gridless numerical method to generate neighboring particle set ma- trix, which can reduce the CPU time to 1/11 of that before introduction. The Bi-CGSTAB （bi-conjugate gradient stabilized） algorithm is applied to solving the Poisson pressure equation, by which the solving speed is significantly accelerated. The process of solitary waves propagating over a numerical flume and interacting with a vertical wall is simulated. The simulated results of water surface elevation are in good agreement with the analytical solution as well as the measured data. The predicted maximum values of the run-up of solitary waves with various relative incident wave heights agree well with the measured results.
